In the present work we demonstrate the application of different physical methods to high-frequency or tick-bytick
financial time series data. In particular, we calculate the Hurst exponent and inverse statistics for the price
time series taken from a range of futures indices. Additionally, we show that in a limit order book the relaxation
times of an imbalanced book state with more demand or supply can be described by stretched exponential laws
analogous to those seen in many physical systems.
By pouring equal balls into a container one obtains disordered packings with fascinating properties which might
shed light on several elusive properties of complex materials such as amorphous metals or colloids. In any real
experiment with equal-sized spheres one cannot reach packing fractions (fraction of volume occupied by the
spheres respect to the total volume, ρ) below the Random Loose Packing limit (RLP, ρ ~ 0.555) or above the
Random Close Packing limit (RCP, ρ ~ 0.645) unless order is externally induced. What is happening at these
two limits is an open unanswered question. In this paper we address this question by combining statistical
geometry and statistical mechanics methods. Evidences of phase transitions occurring at the RLP and RCP
limits are reported.
We construct a correlation-based biological network from a data set containing temporal expressions of 517
fibroblast tissue genes at transcription level. Four relevant and meaningful connected subgraphs of the network,
namely: minimal spanning tree, maximal spanning tree, combined graph of minimal and maximal trees, and
planar maximally filtered graph are extracted and the subgraphs' geometrical and topological properties are
explored by computing relevant statistical quantities at local and global level. The results show that the subgraphs
are extracting relevant information from the data set by retaining high correlation coeffcients. The design
principle of the underlying biological functions is reflected in the topology of the graphs.
One of the main goals in the field of complex systems is the selection and extraction of relevant and meaningful
information about the properties of the underlying system from large datasets. In the last years different methods
have been proposed for filtering financial data by extracting a structure of interactions from cross-correlation
matrices where only few entries are selected by means of criteria borrowed from network theory. We discuss and compare the stability and robustness of two methods: the Minimum Spanning Tree and the Planar Maximally Filtered Graph. We construct such graphs dynamically by considering running windows of the whole dataset. We study their stability and their edges's persistence and we come to the conclusion that the Planar Maximally Filtered Graph offers a richer and more signi.cant structure with respect to the Minimum Spanning Tree, showing also a stronger stability in the long run.
In the recent years, a new wave of interest spurred the involvement of complexity in finance which might provide
a guideline to understand the mechanism of financial markets, and researchers with different backgrounds have
made increasing contributions introducing new techniques and methodologies. In this paper, Markov-switching
multifractal models (MSM) are briefly reviewed and the multi-scaling properties of different financial data are
analyzed by computing the scaling exponents by means of the generalized Hurst exponent H(<i>q</i>). In particular
we have considered H(<i>q</i>) for price data, absolute returns and squared returns of different empirical financial time
series. We have computed H(<i>q</i>) for the simulated data based on the MSM models with Binomial and Lognormal
distributions of the volatility components. The results demonstrate the capacity of the multifractal (MF) models
to capture the stylized facts in finance, and the ability of the generalized Hurst exponents approach to detect
the scaling feature of financial time series.
We investigate complex materials by performing "Virtual Experiments" starting from three-dimensional images of grain packs obtained by X-ray CT imaging . We apply this technique to granular materials by reconstructing a numerical samples of ideal spherical beads with desired (and tunable) properties. The resulting "virtual packing" has a structure that is almost identical to the experimental one. However,
from such a digital duplicate we can calculate several static and dynamical properties (e.g. the force network, avalanche precursors, stress paths, stability, fragility, etc.) which are otherwise not directly accessible from experiments. Our simulation code handles three-dimensional spherical grains and it takes into account repulsive elastic normal forces, frictional tangential forces, viscous damping and gravity. The system can be both simulated within a vessel or with periodic boundary conditions.
The hierarchical structure of correlation matrices in complex systems is studied by extracting a significant sub-set of correlations resulting in a planar graph.
Such a graph has been generated by a method introduced in Aste et al.  and it has the same hierarchical structure of the Minimum Spanning Tree but it contains a larger amount of links, loops and cliques.
In Tumminello et al. , we have shown that this method, applied to a financial portfolio of 100 stocks in the USA equity markets, is pretty efficient in filtering relevant information about the system clustering revaling the hierarchical organization in the whole system and within each cluster.
Here we discuss this filtering correlation procedure and its application to different financial data sets.
The contemporary science of materials and condensed-matter physics is changing in response to a new awareness of the relevance of concepts associated with complexity. Scientists who design and study new materials are confronted by an ever-increasing degree of complexity, both in the materials themselves and in their synthesis. Typically, modern advanced materials are partially non-crystalline, often multicomponent, and form out of equilibrium. Further, they have functional and structural properties that are active over several length-scales. This emerging structural and functional complexity is intrinsic and necessary to many aspects of modern materials; features common also to several other complex systems. In this paper we briefly review the emerging structural complexity in a special model system: sphere packings.
We apply a method to filter relevant information from the correlation coefficient matrix by extracting a network of relevant interactions. This method succeeds to generate networks with the same hierarchical structure of the Minimum Spanning Tree but containing a larger amount of links resulting in a richer network topology allowing loops and cliques. In Tumminello et al.,1 we have shown that this method, applied to a financial portfolio of 100 stocks in the USA equity markets, is pretty efficient in filtering relevant information about the clustering of the system and its hierarchical structure both on the whole system and within each cluster. In particular, we have found that triangular loops and 4 element cliques have important and significant relations with the market structure and properties. Here we apply this filtering procedure to the analysis of correlation in two different kind of interest rate time series (16 Eurodollars and 34 US interest rates).